A tensioner of the pre-cited type is known, for example, from DE-C 40 39 816, wherein the self-adjusting bearing is constituted by a sliding bearing with the cylinder base having a spherical convex sliding surface and the housing bottom having a spherical concave sliding surface. To prevent undesired relative tilting between the piston rod and the cylinder or the guide bush, this float mounting arrangement permits adjusting movements of the cylinder base relative to the housing. This assures an alignment between the guide bush and the piston and between the cylinder and the piston. A drawback of such a float mounting is that a sliding movement between the cooperating spherical sliding surfaces can only take place when their static friction has been overcome. However, when compression springs with high compression pressures are used, it is possible that the balancing movements in the float mounting do not take place because the existing static friction is not overcome. A further drawback resides in the fact that mating convex and concave sliding surfaces involve complicated manufacturing steps and high costs.